Question

the altitude of a right angle triangle is 7 cm less than its base if the hypotenuse is 13 cm find the other two sides

Answer 1

Solution!!

Given that the altitude of the right angled triangle is 7 cm less than its base and the hypotenuse is 13 cm.

Let the base be x.

Altitude = x - 7

Let's apply the Pythagoras Theorem.

(Hypotenuse)² = (Base)² + (Height or Perpendicular)²

(13)² = (x)² + (x - 7)²

169 = x² + x² + 49 - 14x

120 = 2x² - 14x

2x² - 14x = 120

x² - 7x = 60

x² - 7x - 60 = 0

x² + 5x - 12x - 60 = 0

x(x + 5) - 12(x + 5) = 0

(x - 12)(x + 5) = 0

Either x - 12 = 0 => x = 12

Or x + 5 = 0 => x = -5

The value of the base cannot be negative so it's 12 cm.

Base = 12 cm

Height = x - 7 = 5 cm